一种踝关节三维运动空间的量化算法

An Arithmetic for Quantifying the 3D Motion Space of Ankle

目的结合踝关节在各方向上运动之间的约束关系,对其三维转动角度进行积分,得到三维运动空间的大小,用于更加准确全面地量化其灵活度和康复程度。方法选取25例大学生志愿者,其中无踝关节损伤的健康者20例,近期有过踝关节损伤的患者5例。使用运动捕捉系统实时记录被测者脚上标记点的三维坐标。利用三角函数将这些坐标转化为转动角度并进行处理,通过使用多项式拟合,得到踝关节在各个方向上最大转动角度随跖屈和背屈角度变化的方程。对拟合得到的方程进行积分,得到踝关节三维运动空间的大小。结果健康人群踝关节的三维运动空间为41.256,个体间差距小于10%。患者患侧三维运动空间的大小为33.163,由于康复程度的不同,个体间差距小于15%。两组之间存在显著性差异(t=8.804,P<0.01)。在同一跖屈和背屈角度下,内翻的最大转动角度比外翻大,内旋的最大转动角度比外旋大。结论通过此算法能更准确地量化踝关节三维运动空间的大小,实现对踝关节灵活度和康复程度更全面的评估。

Objective To obtain the three-dimensional(3D)motion space of ankle by an integral for the3D rotation angle with mutualrelationships of rotation angles in different directions,which is used to evaluate the flexibility and recovery of ankle more accurately and fully.Methods Twenty-five graduate students were recruited to participate in this study,one group consisted of20healthy individuals withoutankle injury,and the other was composed of5patients with ankle injury.A motion capturing system was used to simultaneously capture the3D coordinates of the marked points on the foot.Next,these3D coordinates were converted into rotation angles through trigonometric functionsprocessed.The maximum rotation angles of adduction,abduction,varus,and eversion change with the rotation angles of plantar flexionand dorsal flexure were measured by using polynomial fitting.At last,the size of the ankle's3D motion space was obtained by integratingthe fitting functions.Results The ankle's3D motion space of the healthy people was41.256,and the variation among them was less than10%.The ankle's3D motion space of the patient side was33.163,and the variation among them was less than15%because of the differentdegrees of rehabilitation.There was significant difference between two groups(t=8.804,P<0.01).With the same rotation angles of plantarflexion or dorsal flexure,the maximum rotation angle of varus was larger than that of eversion,and the maximum rotation angle of adductionwas larger than that of abduction.Conclusion The algorithm can be used to quantify the3D motion space of ankle more accurately,andto achieve a more comprehensive evaluation of ankle's flexibility and rehabilitation.